Turkish Prime Minister Binali Yildirim says his country's troops have crossed over the Syrian border on the second day of Ankara's operation on a Kurdish-run enclave, which responded by firing rockets at Turkish towns.

Yildirim said on January 21 that the troops crossed into the Afrin region, which is controlled by the Syrian Kurdish YPG militia, Turkish media reported.

They said that the Turkish forces were advancing alongside forces from the Free Syrian Army (FSA).

The number of the Turkish soldiers involved in the offensive was not specified.

Yildirim was quoted as saying that the operation aimed to create a security zone some 30 kilometers deep inside Syria.

On January 21, the United States urged Turkey to exercise restraint and ensure that the offensive is "limited in scope and duration."

The Syrian government, Iran and Egypt condemned the attack, which activists said has killed at least 18 civilians in Afrin in the first 24 hours. Turkish officials say 11 rockets launched from Syria have landed in Turkish towns along the border, killing at least one Syrian refugee and injuring 47.

Diplomats at the United Nations said the Security Council, at France's request, will on January 22 hold closed-door discussions on the worsening situation in Syria after the Turkish offensive.

France urged Turkish authorities "to act with restraint in a context where the humanitarian situation is deteriorating in several regions of Syria."

Turkish forces on January 20 began the exercise which seeks to oust the U.S.-backed YPG militia from Afrin, despite U.S. warnings that such a move could further destabilize the area.

The Turks accuse the YPG of having links to the outlawed Kurdistan Workers Party (PKK), which has waged an insurgency in southeast Turkish for more than 30 years. The PKK is regarded as a terror group by Turkey, the United States, and the European Union.

The Turkish military said 153 Kurdish militant targets had been hit by Turkish artillery and warplanes, including shelters, hideouts, and arsenals used by the militants.

Early on January 21, Turkish officials said four rockets struck the border town of Kilis, slightly wounding one person and damaging two houses and an office. Turkish artillery returned fire.

Kurdish militia officials earlier said at least 10 people, mostly civilians, were killed in dozens of Turkish air attacks in the Afrin region.

"Seven civilians were killed, including a child, as well as two female fighters and one male fighter," Birusk Hasakeh of the YPG militia told the AFP news agency.

The PYD, the YPG’s political branch, said 25 civilians had been wounded in bombing attacks by Turkish warplanes.

Turkish officials confirmed there had been casualties, but said they were all members of Kurdish militias.

Yildirim said on January 20 that air strikes targeting the Afrin enclave were aimed at eliminating "elements" of the YPG in Syria and Islamic State (IS) militants.

Earlier that day, Turkish President Recep Tayyip Erdogan said the “Olive Branch” military operation had begun in Afrin and that another operation in nearby Manbij would follow.

The Turkish army said the Minnigh military airport north of Aleppo, held by the YPG, had been among the targets hit by air strikes.

Officials said IS targets were also destroyed and that all warplanes returned safely.

Turkish officials said Foreign Minister Mevlut Cavusoglu had spoken by telephone with U.S. Secretary of State Rex Tillerson and that Turkey's top general, Hulusi Akar, informed his U.S. and Russian counterparts of the operation.

The Russian Foreign Ministry said on January 21 that Foreign Minister Sergei Lavrov and Tillerson discussed the Syrian conflict in a telephone call, in particular ways to bring stability to the country's north.

The State Department said Tillerson had spoken with Lavrov as well as Cavusoglu to express U.S. concern about the situation.

While supporting Ankara's legitimate security concerns, "we urge Turkey to exercise restraint and ensure that its military operations remain limited in scope and duration and scrupulous to avoid civilian casualties," State Department spokeswoman Heather Nauert said in a statement.

Turkish moves against the YPG will likely raise tensions with the United States, a NATO ally.

The United States relies on the YPG in its fight against IS militants in Syria and it has announced plans to form a U.S.-backed border security force of 30,000 personnel in northern Syria, partly consisting of YPG fighters.

The Russian Defense Ministry said it was withdrawing its troops from the Afrin area to “prevent potential provocation and exclude the threat to the life and well-being of the Russian military."

Russia has given Syrian President Bashar al-Assad's government crucial military backing in recent years, which has killed hundreds of thousands of people and displaced millions since it began with a state crackdown on pro-democracy protesters in March 2011.

The Syrian government condemned what it called "Turkish aggression on Afrin," Syrian state media reported on January 20.